The  Interpretation  of 
Railway  Statistics 


Of 


Ernest  Ritson  Dewsnup 

Professor  of  Railway  Administration  in  the  Univer¬ 
sity  of  Illinois 


Reprinted  from 

Itoilroag^grfe'ttr 


May  13,  1910 


^  o  o  .  v\  Vj 

D  S'/S'* 

[ttleprint  from  Railway  Aye  Gazette,  May  13,  1910.] 

THE  NECESSITY  OF  CARE  IN  THE  INTERPRETATION 
OF  RAILWAY  STATISTICS  USED  COMPARATIVELY. 

The  growth  in  importance  of  the  railway  has  given  to  its 
statistics  a  publicity  and  a  popularity  hardly  exceeded  by  those 
of  any  other  economic  undertaking,  and  of  no  country  is  this 
truer  than  the  United  States.  Governmental  activity  has  been 
a  stimulating  cause  of  this  abundance  of  information,  but  the 
railways  themselves  have  come  to  realize  that  it  is  good  policy 
to  be  less  reserved  in  their  relations  with  the  public  than  they 
have  been.  Thus,  a  much  larger  amount  of  information  has 
been  made  accessible  than  government  schedules  have  called 
for.  The  facts  available,  however,  have  not  always  been  ana¬ 
lyzed  with  due  discrimination.  Statistical  material  is  highly 
dangerous  to  handle,  and  even  those  familiar  with  its  treat¬ 
ment  have  to  act  with  the  utmost  wariness  and  discretion. 
Its  way  is  not  so  plain  that  a  wayfaring  man,  though  a  fool, 
need  not  err  therein.  Defective  comparison,  arising  out  of 
the  omission  of  vital  facts,  is  common.  Certain  more  or  less 
traditional  methods  of  presentation  are  followed  that  assume 
to  carry  with  them  illuminating  exposition  of  vital  points  of 
railway  development  and  operation,  but  are  more  remarkable 
for  what  they  fail  to  tell  than  for  anything  they  do  tell. 
Brevity  is  the  soul  of  wit  in  railway  statistics  as  elsewhere, 
but  it  can  be  pushed  to  the  verge  of  obscurity  and,  quite 
frequently,  to  the  point  of  insufficiency.  Another  class  of 
defects  in  statistical  comparison  arises  from  a  lack  of  appre¬ 
ciation  of  the  real  significance  of  the  data  used :  the  statistician 
fails  to  make  himself  acquainted  with  the  intrinsic  worth  of 
his  figures.  Nothing  can  be  more  inimical  to  the  soundness 
of .  statistical  logic  than  a  hasty  acceptance  of  material  used 
at  its  superficial  value.  It  is  absolutely  essential  to  scrutinize 
rigidly  methods  of  compilation.  Carelessness  or  oversight  in 
this  connection  is  responsible  for  many  erroneous  analyses 
and  vicious  comparisons.  The  following  pages  contain  a 
brief  review  of  some  of  the  more  important  railway  statistics 
in  the  use  of  which  for  comparative  purposes  the  writer  has 
observed  more  or  less  serious  errors.  Some  of  the  points 
touched  upon  raise  issues  of  considerable  dispute,  and,  if  it 
seems  that  such  are  treated  too  cavalierly,  it  must  be  remem¬ 
bered  that  this  is  inevitable  in  a  general  treatment  of  re¬ 
stricted  length;  at  a  subsequent  time  it  may  be  possible  to 
discuss  these  issues  more  in  detail. 

FREIGHT  HOUSE  TONNAGE  COSTS. 

A  good  example  of  the  difficulties  besetting  the  path  of  the 
statistician  without  adequate  technical  knowledge  of  his  facts 
Is  to  be  found  in  freight  house  tonnage  costs.  Freight  house 
operation  seems  to  be  very  similar,  in  a  general  kind  of  way, 
wherever  it  is  carried  on,  and,  therefore,  fairly  capable  of  being 
measured  as  to  its  efficiency  by  the  actual  per  ton  costs  of 


3 


handling.  As  a  matter  of  fact,  however,  while  a  ton  of  freight 
is  a  uniform  unit  so  far  as  mere  weight  goes,  it  is  a  very  vari¬ 
able  one,  indeed,  with  respect  to  its  handling.  One  consignment 
of  freight  may  require  twice  as  much  handling  as  another  of 
equal  weight.  Thus  a  ton  of  general  merchandise  will  consume 
more  of  the  working  time  of  weighers,  truckers  and  stowers  than 
a  ton  of  iron  bars.  And  a  ton  of  merchandise  in  twenty  differ¬ 
ent  packages  will  be  a  longer  handling  proposition  than  a  ton 
of  similar  freight  in  five  packages.  Freight  houses  called  upon 
to  handle  large  quantities  of  mail-order  house  shipments 
usually  have  this  factor  of  increased  cost  to  contend  with,  no 
small  amount  of  such  business  being  in  very  small  packages, 
consigned  to  an  innumerable  variety  of  addresses.  Dissimi¬ 
larity  in  the  nature  of  the  freight  handled  manifests  itself  to 
the  highest  degree  in  the  railway  terminals  of  districts  with 
different  producing  interests,  but  it  may  be  found  in  terminals 
located  in  the  same  district,  and,  to  the  extent  that  it  exists, 
renders  tonnage  costs  entirely  unreliable  as  a  test  of  relative 
efficiency.  I  have  heard  of  this  consideration  being  ignored 
even  by  railway  officers  in  comparing  the  tonnage  costs  of 
freight  stations  at  different  points  on  the  lines  under  their 
jurisdiction.  The  officers  concerned  were  perhaps  relatives  of 
the  newly-appointed  division  superintendent  who,  being  re¬ 
quested  by  shippers  on  his  division  to  provide  them  with 
double  decker  cars,  objected  on  the  ground  of  the  expense  that 
would  be  involved  in  raising  the  bridges. 

Another  element  with  an  important  influence  upon  tonnage 
cost  is  the  size  of  the  freight  business  handled.  The  small 
freight  house  seems  able  to  give  an  appreciable  lead  to  its 
bigger  brother  in  handling  costs,  this  arising  largely  from 
the  fact  that  the  bigger  freight  house  required  for  the  busi¬ 
ness  of  the  latter  increases  the  trucking  that  has  to  be  done. 
It  ought  to  be  possible,  however,  to  offset  much,  if  not  all,  of 
this  increase  by  the  introduction  of  mechanical  appliances  in 
the  larger  houses,  but,  so  far,  American  freight  houses  are  not 
remarkable  for  their  achievements  in  this  direction.  The 
more  important  English  terminals,  it  is  interesting  to  note, 
have  made  considerable  progress  in  the  utilization  of  hydraulic 
and  electrical  power. 

Where  delivery  of  freight  is  undertaken  or  arranged  for  by 
the  railways,  local  conditions  may  cause,  at  some  stations,  an 
abnormal  amount  of  rehandling,  which,  of  course,  leaves  its 
mark  upon  the  tonnage  costs.  Variations  of  cost,  arising 
from  such  cause,  do  not  exist  in  this  country  to  the  extent 
that  they  do,  for  instance,  in  England.  In  very  rare  instances 
do  railways  here  undertake  the  delivery  of  freight.  But  it  is 
essential  to  bear  in  mind  this  rehandling  element  of  cost  when 
comparing  American  with  English  performances  or  the  costs 
of  various  English  goods  depots.  At  some  important  points 
in  England  the  amount  of  warehousing,  as  it  is  termed,  is 
considerably  above  the  normal,  an  appreciable  portion  of  the 


4 


inward  freight,  instead  of  being  sent  out  directly  by  the 
wagons  of  the  company  or  of  its  carting  agents,  having  to  be 
raised  by  crane  to  a  second,  third,  or  even  fourth,  story, 
trucked  over  a  floor  often  of  large  area,  with  the  reverse 
operation  to  be  gone  through  when  the  consignee  calls  for  the 
freight.  Sometimes  the  agent  is  allowed  extra  tonnage  on 
this  warehousing  for  the  purpose  of  making  costs  comparable; 
thus,  for  every  ton  warehoused,  a  ton  and  a  half,  say,  would  be 
reckoned  in  computing  the  average  cost,  but  this  practice  is 
by  no  means  universal. 

Tonnage  costs  as  between  one  terminal  and  another  may 
be  affected  by  differences  in  the  quality  of  labor  available  for 
freight-house  work.  Should  it  happen  that  the  labor  environ¬ 
ment  of  two  terminals  differed  very  materially,  it  would  be 
unfair  to  the  local  management  at  the  less  favorably  situated 
one  to  accept  tonnage  costs  as  indicative  of  relative  efficiency 
without  adjustment  being  made  for  this  difference.  Occa¬ 
sionally  very  special  labor  conditions  introduce  a  still  further 
disturbing  element.  I  cannot  think  of  a  better  illustration 
than  the  casual  labor  so  effectively  made  use  of  at  several 
of  the  London  goods  depots.  Where  labor  of  this  kind  can  be 
procured  but  a  minimum  full-time  or  regular  working  force 
needs  to  be  maintained,  the  casual  labor,  waiting  around  the 
office  for  a  job,  being  brought  in  for  the  busy  period  at  a 
comparatively  low  rate  of  wage  per  hour.  Ordinarily,  such 
labor  would  be  regarded  as  unreliable  and  inefficient  for  the 
class  of  work  to  be  done,  but  in  London  this  does  not  seem  to 
be  the  case.  In  fact,  a  considerable  number  of  these  men  be¬ 
come  more  or  less  regular  “half-timers,”  and  vacancies  in  the 
full-time  force  are  filled  from  their  ranks  quite  frequently. 
Strange  as  it  may  appear  it  sometimes  happens  that  such 
promotion  is  refused,  the  chosen  ones  preferring  the  compara¬ 
tively  go-as-you-please  conditions  of  casual  employment  to  the 
more  rigid  requirements  of  regular  work.  The  result  of  such 
labor  arrangements  is  to  enable  the  terminals  thus  advan¬ 
tageously  situated  to  keep  their  tonnage  costs  far  below  what 
they  would  normally  be. 

Freight-house  costs,  it  is  hardly  necessary  to  observe,  may 
be  “in”  or  “out;”  that  is  to  say,  the  costs  of  working  inbound 
or  outbound  freight.  The  two  are  essentially  distinct.  Under 
normal  conditions,  the  cost  of  working  inbound  freight  should 
run  lower  than  that  of  outbound,  since  the  former  freight  can 
be  unloaded  with  greater  dispatch  and  less  irregularly  than  is 
the  case  with  the  corresponding  operations  of  loading. 

Tonnage  costs  are  commonly  relied  upon  as  a  fair  basis  for 
the  comparison  of  efficiency  in  the  same  freight-house  from 
period  to  period,  and,  as  a  rule,  justifiably  so.  But,  even  in 
this  case,  the  value  of  the  comparison  depends  upon  the 
absence  of  change  in  the  general  nature  of  the  tonnage  han¬ 
dled  as  well  as  on  other  conditions.  But  traffic  conditions 
alone  being  taken  into  account,  it  is  quite  possible  that  a 


5 


change  in  these  might  increase  tonnage  costs,  say,  from  35c. 
to  37c.  a  ton,  in  spite  of  a  real  improvement  in  the  working 
efficiency  of  the  house  during  the  period  of  comparison. 

From  what  has  been  said  it  appears  very  evident  that  as  a 
comparative  measure  of  relative  efficiency  of  management  the 
tonnage  cost  of  handling  may  prove  to  he  a  very  misleading 
guide,  especially  when  applied  to  different  terminals,  but,  at 
times,  even  when  applied  to  .the  same  terminal. 

YAED  CAE  COSTS. 

Yard  car  costs  also  require  considerable  care  in  their  use. 
As  a  test  of  relative  skill  of  management,  they  fail  because 
of  the  differences  in  labor  quality,  in  nature  of  work  to  be 
done,  in  the  physical  condition  of  the  yard,  in  climatic  and 
other  conditions.  But  they  may  be,  and  frequently  are,  ren¬ 
dered  entirely  useless  for  statistical  purposes  because  of  the 
lack  of  a  uniform  system  in  compiling  them.  Thus,  some  ter¬ 
minals  base  their  yard  costs  per  car  upon  the  number  of  cars 
received  and  forwarded  in  trains  and  received  from  and  de¬ 
livered  to  connecting  lines.  In  other  cases,  not  only  these  car 
movements  are  included,  but  also  many  of  the  internal  move¬ 
ments,  such  as  cars  to  and  from  transfer  tracks,  cars  to  and 
from  team  tracks,  and  so  on.  This  difficulty  as  to  what  prop¬ 
erly  constitutes  a  car  movement  could  be  overcome  by  agree¬ 
ment,  but  at  the  present  time  it  still  presents  a  serious  ob¬ 
stacle  to  the  successful  comparison  of  yard  costs  as  they  are 
actually  furnished  by  different  terminals.  In  every  case,  it  is 
necessary  to  go  behind  the  figures  given  and  to  analyze  their 
method  of  compilation. 

PASSENGEE  AND  TON-MILEAGE  COSTS. 

Passenger  and  ton-mileage  costs  have  been  made  much  use 
of  by  practical  men  and  by  theorists,  but,  frequently,  with 
a  careless  disregard  of  the  limits  of  their  usefulness.  More 
than  one  writer  has  been  content  to  assume  the  propriety 
of  measuring  the  general  operating  efficiency  of  one  railway 
system  against  that  of  another  by  means  of  the  costs  of  opera¬ 
tion  per  passenger  or  per  ton  per  mile.  Such  a  comparison 
is  too  unreliable  to  be  depended  upon  as  a  guide  to  relative 
efficiency.  It  takes  for  granted  that  labor,  physical,  traffic 
and  other  conditions  are  fairly  similar,  though,  in  fact,  they 
are  frequently  extremely  dissimilar.  To  say  that  one  road 
operates  its  freight  traffic  at  eight-tenths  of  a  cent  per  ton- 
mile  and  another  road  at  six-tenths  of  a  cent  is  to  throw 
absolutely  no  light  upon  the  skill  with  which  the  freight 
traffic  of  the  respective  roads  is  worked.  The  road  with  the 
higher  ton-mile  cost  may  be  the  one  most  efficiently  operated. 
The  only  real  value  of  such  traffic  mileage  costs  is  in  keep¬ 
ing  track  of  the  movement  of  operating  costs  on  the  same 
railway,  or,  preferably,  on  the  individual  divisions  compris¬ 
ing  a  railway.  I  say  preferably,  as  regards  the  latter,  be¬ 
cause  the  general  average  for  the  railway  as  a  whole  may 
have  remained  unchanged  over  the  period  of  investigation 


6 


and  yet  the  real  operating  conditions  may  have  materially 
altered,  progression  on  some  divisions  being  counterbalanced 
by  retrogression  on  other  divisions.  Even  within  the  limits 
of  a  single  railway  it  may  be  decidedly  unfair  to  measure 
the  operating  results  of  one  division  against  those  of  an¬ 
other — conditions  must  be  substantially  similar  before  cost 
results  can  be  accepted  as  the  basis  of  such  a  comparison. 

The  value  of  ton-mile  costs  has  been  emphasized  by  some 
because  of  a  belief  that  they  afford  a  scientific  basis  for  the 
establishment  of  reasonable  rates.  Yet,  it  is  not  possible  to 
allocate,  other  than  by  arbitrary  pro-rates,  more  than,  at 
the  most,  about  75  per  cent,  of  even  the  transportation  and 
maintenance  costs  to  the  respective  freight  and  passenger 
services.  And  since,  as  a  matter  of  practical  necessity,  a 
railway  must  pay  interest  on  funded  debt,  interest  on  current 
liabilities,  rents  for  leased  lines,  taxes,  and,  for  future  pro¬ 
tection,  permanent  improvement  expenditures  charged  to  in¬ 
come,  there  still  remains  nearly  30  per  cent,  of  the  total 
expenditures,  esrential  to  the  working  of  the  system,  which 
again  can  be  allocated  only  on  a  more  or  less  arbitrary  pro¬ 
rating  basis.  Thus,  close  upon  half  of  the  annual  costs  of 
maintaining  a  railway  organization  and  securing  its  opera¬ 
tion  are,  in  the  present  state  of  our  knowledge  of  railway 
costs,  incapable  of  being  accurately  divided.  The  actual  cost 
might  vary  materially  from  the  pro-rated  cost,  and,  to  the  ex¬ 
tent  of  this  variation,  the  reliability  of  the  latter  as  a  crite¬ 
rion  wrould  be  impaired. 

But  even  if  it  were  practicable  to  allocate  to  the  freight 
service  as  a».whole  its  proper  proportion  of  costs,  it  would 
still  be  a  far  cry  to  the  distribution  of  these  costs  between 
the  multitude  of  commodities  transported  by  the  railway 
under  very  varying  conditions  of  speed,  equipment  facilities, 
terminal  handling  and  so  forth.  There  are  some  happily-dis- 
positioned  writers  and  regulative  bodies  who  see  all  these 
difficulties  vanishing  into  thin  air  when  resort  is  had  to  some 
magical  pro-rating  basis  as  train  mileage  or  gross  ton-mile¬ 
age,  or  the  like.  These  engineers  of  philosophy  are  so  much 
in  advance  of  many  of  us  poor  mortals  that  they  have  no 
trouble  in  determining  the  roadway  maintenance  expense  due 
to  a  50-mile  an  hour  500-ton  through  express  passenger  train? 
as  compared  with  that  due  to  a  12-mile  an  hour  2,500-ton 
freight  train,  stopping,  maybe,  at  almost  every  siding.  Their- 
attitude  is  picturesque,  but  unconvincing. 

It  should  be  said  further  that  if  an  allocation  of  costs  to; 
each  unit  of  freight  could  be  satisfactorily  made,  the  problem 
of  reasonableness  would  still  remain  unsettled.  The  theory- 
of  reasonable  rate  determination  with  reference  to  traffic  mile¬ 
age  costs  means,  I  take  it,  the  fixing  of  a  rate  at  a  figure  al¬ 
lowing  a  reasonable  rate  of  profit  above  cost  of  operation; 
but,  as  a  practical  proposition,  how  is  the  latter  to  be  de¬ 
termined?  It  should  certainly  be  reasonably  related  to  the 


7 


risks  and  difficulties  of  the  business,  but  who  is  to  fix  the 
specific  nature  of  that  relation?  Are  the  risks  of  railway 
business  equal  to,  less  than,  or  greater  than,  those  of  bank¬ 
ing,  insurance,  steel  manufacture?  If  not  identical,  what  per¬ 
centage  of  variation  in  profits  will  represent  the  variation  in 
risk?  Again',  absolutely  uniform  efficiency  of  management 
cannot  be  expected,  and  uniformity  of  working  environment 
is,  of  course,  impossible.  Hence,  one  series  of  railway  opera¬ 
tions  under  control  of  railway  company  X  will  be  handled 
much  more  economically  than  a  corresponding  series  con¬ 
trolled  by  railway  company  Y,  resulting  in  a  lower  cost  per 
unit  of  traffic.  Is  X  to  be  allowed  to  charge  rates  similar 
to  Y,  and,  if  so,  is  the  extra  large  profit  it  secures  as  a  re¬ 
sult  of  its  greater  efficiency  a  reasonable  rate  of  profit?  On 
the  other  hand,  if  its  rates  are  adjusted  so  as  to  reduce  its 
rate  of  profit  to  the  same  level  as  that  of  Y,  will  there  not 
result  territorial  rate  discrimination  quite  as  clear-cut  as  any¬ 
thing  that  occurs  under  the  present  commercial  system  of 
rate  making? 

TRAIN  AND  ENGINE-MILE  AVERAGES. 

Other  interesting  operating  statistics  are  train  and  engine- 
mile  averages,  which,  in  their  general  form,  have  less  utility 
than  some  would  ascribe  to  them.  A  passenger  train-mile 
covers  everything  from  the  more  or  less  dilapidate^  crawling 
local  on  branch  lines  to  60  miles  an  hour  luxuriously  ap¬ 
pointed  expresses  on  the  main  line,  from  a  train  of  an  engine 
and  one  car  to  one  with  a  dozen  or  more  cars.  Similarly,  the 
freight  train  mile  coerces  into  statistical  uniformity  the 
humblest  way  freight  with,  perhaps,  a  total  weight  of  a  couple 
of  hundred  tons  behind  the  tender  to  the  lOlT-car,  3,000-ton 
train;  it  connects  the  slow  “dead”  freight  train  with  the  high¬ 
speed  “manifest”  train:  coal  train,  live  stock,  merchandise 
train — all  are  indiscriminately  mingled  in  the  average.  An 
arithmetical  average  is  obtained,  it  is  true,  but  one  of  treach¬ 
erous  utility,  unless  environed  by  a  galaxy  of  interpreting, 
modifying  and  saving  clauses,  only  to  be  used  by  the  initiated, 
and  even  then  with  the  greatest  circumspection. 

It  is  still  customary,  on  the  part  of  some  transportation 
students,  to  depend  upon  engine  mileage  as  a  reliable  basis 
upon  which  to  establish  comparative  efficiency  statistics  of  an 
important  brand  of  railway  operation.  The  value  of  such 
statistics  depends  very  largely  upon  the  way  in  which  they 
are  put  together.  But  general  averages  of  engine-mile  costs 
can  hardly  be  regarded,  under  any  conditions,  as  affording 
the  means  of  drawing  conclusions  of  any  practical  worth. 
The  engine-mile,  in  its  general  form,  is  itself  variable.  Its 
elements  may  be  freight  or  passenger  or  switching  engine, 
high-speed  Atlantic  or  low-speed  consolidations,  with  tractive 
powers  of  infinite  variety.  Obviously,  when  such  engine  mile 
age  is  used  as  a  measure  of  costs,  it  fails  lamentably  to  serve 
any  useful  purpose.  To  do  this  it  must  be  limited  to  engines 


of  the  same  general  class,  and  even  then  its  definiteness  is 
not  altogether  satisfactory.  Clearly,  a  compound  unit  of  per¬ 
formance  which  allows  for  the  influences  of  physical  con¬ 
ditions,  such  as  gradient  and  curvature,  and  also  for  speed,  is 
the  only  sort  of  unit  really  suitable  even  in  a  restricted 
analysis  of  engine  mileage  costs.  Uniform  units  of  work  done 
need  to  be  established  and  engine  costs  related  to  these;  this 
the  engine-mile  average  fails  to  do. 

FREIGHT  CAR  TON  MILEAGE. 

Freight  car  efficiency  is  a  matter  of  great  railway  interest 
and  its  proper  measurement  seems  to  be  logically  based  upon 
the  performance  of  the  average  car  in  loaded  car  miles.  The 
calculation  of  this  would  ordinarily  be  a  very  simple  process, 
namely,  the  division  of  the  total  ton  mileage  by  the  number 
of  cars  employed.  Unfortunately  for  the  student  of  railway 
reports,  it  is  rot  obtainable  so  easily  as  one  would  suppose 
from  the  foregoing.  In  the  first  place,  the  freight  cars  re¬ 
ported  as  ‘owned,  both  in  the  statistics  furnished  in  the  annual 
reports  of  the  Interstate  Commerce  Commission  and  in  very 
many  railway  reports,  are  those  owned  on  the  last  day  of  the 
fiscal  year.  It  is  obvious  that  the  loaded  car  miles  are  made 
by  the  actual  cars  in  operation,  some  of  which  have  been  in 
service  throughout  the  year,  others  for  less  periods  varying 
from  several  months  to  but  a  few  days.  Evidently,  the  equiva¬ 
lent  number  of  cars  owned  throughout  the  year  is  required 
as  the  divisor,  otherwise  the  quotient  will  be  more  or  less 
inaccurate  as  a  test  of  efficiency.  In  the  second  place,  the 
ton  mileage  reported  is  the  result  of  work  done  both  by  home 
and  foreign  cars.  Cases  have  been  known  in  which  the  cars 
upon  the  lines  of  a  railway  have  exceeded  b^  as  much  as  one 
hundred  per  cent,  the  number  owned  by  it.  Under  such  con¬ 
ditions,  even  if  the  equivalent  number  of  cars  owned  through¬ 
out  the  year  were  available,  the  quotient  of  total  ton  mileage 
divided  by  the  same  would  be  very  far  from  representing  the 
exact  work  of  the  cars.  Of  course,  in  dealing  with  statistics 
of  the  United  States  as  a  whole,  this  possible  source  of  error 
disappears  except  in  so  far  as  car  relations  with  Canada  and 
Mexico  affect  the  situation,  and  any  disturbance  of  results 
from  such  would  be  so  small  as  to  be  negligible.  In  the  third 
place,  reported  ton  mileage  is  made  up  of  tonnage  hauled  by 
the  railway  both  in  its  own  cars  and  in  privately  owned  cars. 
Here  again  it  is  apparent  that  the  car  ton  mileage  obtained 
in  the  usual  fashion  is  in  error.  The  private  cars  working 
the  ton  mileage  need  to  be  included,  or  better,  for  purposes 
of  the  comparison  of  efficiency  of  the  freight  car  operation  of 
different  roads,  the  ton  mileage  of  private  cars  excluded.  The 
latter  is  preferable  because  of  the  special  conditions  surround¬ 
ing  certain  classes  of  private  car  movement,  ensuring  fre¬ 
quently  a  superior  performance  to  that  of  the  railway  owned 
car,  and,  further,  because  of  the  differences,  as  between  rail¬ 
ways,  in  the  extent  of  this  private  car  traffic. 


But  supposing  that  all  these  difficulties  in  the  determination 
of  freight  car  performance  are  satisfactorily  met,  the  greatest 
caution  is  still  required  in  interpreting  the  results.  It  is  quite 
conceivable  that  a  lower  ton  mileage  average  may  represent 
as  great  or  greater  operating  efficiency  on  the  part  of  the  rail¬ 
way  concerned  as  the  higher  one  of  another  road.  This  arises 
out  of  the  varying  influence  on  mileage  of  different  species  of 
traffic.  The  larger  the  proportion  of  local  freight  traffic,  the 
lower  will  tend  to  be  the  mileage  made,  but  the  reduced  ton 
mileage  average  by  no  means  infers  less  efficiency.  Again,  the 
existence  of  an  unusually  large  percentage  of  colliery  traffic 
will  ordinarily  exercise  a  depressive  influence  upon  the  ton 
mileage,  on  account  of  mine  delays  and  unloading  time  allow¬ 
ances.  Demurrage  regulations  are  also  a  factor  not  to  be 
overlooked  in  deducing  results  from  ton  mileage  performances, 
of  railways  situated  in  different  territories.  If  the  legal  loan¬ 
ing  or  unloading  free  time  is  48  hours  in  the  territory  of  one 
road  and  96  hours  in  the  territory  of  another,  mileage  move¬ 
ment  in  the  latter  case  is  restricted.  The  restriction  is  not 
effective  to  the  extent  of  the  difference  in  legal  time,  it  may 
be  noted,  since  there  would  be  in  both  territories  a  large  num¬ 
ber  of  shippers  who  would  not  make  use  of  the  legal  maximum. 

THE  OPERATING  RATIO. 

The  operating  ratio  is  generally  accepted  as  a  statistic  of 
great  value.  Yet  in  the  usual  form  of  the  percentage  of  total- 
annual  operating  expenditure  to  total  annual  operating  rev¬ 
enue,  its  value  is  liable  to  exaggeration.  The  same  operating 
ratio  may  conceal  any  number  of  changes  in  efficiency  of  per¬ 
formance  from  year  to  year.  Thus,  in  a  certain  year,  extrava¬ 
gant  operation  during  the  season  of  light  traffic  may  be  coun¬ 
terbalanced  by  an  abnormal  increase  of  business  during  the 
period  of  heavy  traffic,  with  the  result  that  the  operating  ratio 
stands  at  the  same  level  as,  or  even  lower  than,  in  the  previous 
year  when,  say,  greater  uniform  efficiency  of  operation  was 
obtained  throughout  the  year.  The  general  operating  ratio 
may  frequently  fail  to  indicate  movements  in  maintenance 
of  roadway,  maintenance  of  equipment,  traffic,  conducting 
transportation,  and  general  administration,  in  which  consid¬ 
erable  variations  may  occur  and  yet  leave  no  record  in  the 
general  ratio.  The  mere  statement  that  the  operating  ratio 
is  this  and  that  in  years  of  comparison  is  meaningless  from 
the  point  of  view  of  operating  efficiency  until  most  careful 
scrutiny  is  made  of  its  component  factors.  An  increase  in  it 
may  cover  greater  efficiency,  a  decrease  relatively  greater  in¬ 
efficiency,  and  a  stationary  position  either  one  or  the  other. 

Error  can  easily  be  made  in  comparing  operating  ratios  of 
different  systems  by  reason  of  opposed  financial  policies  in  the 
roads  compared.  For  example,  the  ratios  are  not  comparable 
in  the  case  of  two  systems,  one  of  which  charges  as  much  of 
permanent  improvement  expenditure  as  possible  to  repairs 
account  and  the  other  as  little  as  possible. 


10 


PASSENGER  ACCIDENT  AVERAGES. 

Passenger  train  accident  figures  are  of  all  railway  statistics 
the  ones  which  are  most  profusely  presented  to  and  .most 
eagerly  devoured  by  the  public.  It  goes  without  saying  that 
the  presentation  of  numbers  of  killed  and  injured  without 
reference  either  to  the  conditions  out  of  which  the  accidents 
arose  or  to  the  relation  of  these  numbers  to  the  traffic  is  a 
very  partial  and  defective,  therefore  improper,  method  of 
comparing  safety  in  travel  on  different  systems.  Nor  are 
such  averages  as  number  killed  and  number  injured  per  so 
many  passenger  journeys  of  appreciable  value  in  endeavoring 
to  measure  the  relative  frequency  of  accident. 

It  is  necessary,  in  the  first  *place,  to  segregate  accidents 
arising  out  of  passenger  train  movement  and  beyond  the  con¬ 
trol  of  the  passenger,  from  the  rest,  and,  in  the  second  place,, 
to  average  these  accidents  upon  the  passenger  train  mileage, 
so  many  accidents  per  one  million  train  miles,  and,  associated 
with  this  average,  should  be  the  average  number,  killed  and 
average  number  injured  pe‘r  one  million  train  miles.  The 
latter  figures  emphasize  the  waste  of  human  life  and  efficiency, 
but  to  my  mind  the  former  averages  are  the  more  valuable. 
The  number  killed  and  injured  in  a  collision  or  derailment  is 
almost  a  pure  matter  of  chance,  influenced  by  car  structure, 
by  presence  of  inflammmable  oils,  live  coals,  etc.,  by  distribu¬ 
tion  of  passengers  in  the  cars,  and  by  other  circumstances. 
An  accident  that,  by  all  theory,  ought  to  have  caused  the  most 
serious  disaster  may  be  trifling  in  its  effect;  an  accident  that 
normally  would  have  produced  a  few  injuries  may,  unex¬ 
pectedly,  result  in  lamentable  loss  of  life.  So  that  really, 
relative  efficiency,  in  the  matter  of  avoiding  accidents  in  pas¬ 
senger  traffic,  would  be  shown  best,  not  by  reference  to  persons 
killed  and  injured,  but  by  the  number  of  train  accidents  per 
million  passenger  train  miles,  and  such  figures  would  form  a 
desirable  addition  to  every  report  of  railway  accidents.  Rail¬ 
ways  have  a  natural  aversion  to  display  their  weaknesses  in 
the  form  of  train  accidents,  but  it  would  exert  a  beneficial 
influence  upon  them  if  they  were  required  half  year  by  half 
year  to  publish  in  the  leading  daily  papers  a  full  statement 
on  oath  showing  the  relationship  of  their  accident  roll  during 
the  period  to  the  amount  of  traffic  they  handle.  At  the  same 
time  it  would  be  unfair  to  the  railways  to  pass  on  without 
saying  that  several  roads  have  been  and  are  devoting  great 
attention  to  the  removal  of  the  causes  of  accidents.  Surprise 
checking,  public  investigations,  and  so  on,  are  some  of  the 
methods  that  promise  satisfactorily. 

MILEAGE  STATISTICS. 

Little  need  be  said  here  about  mileage  statistics.  It  is  obvi¬ 
ously  inaccurate  to  compare  the  extent  of  railway  systems  by 
route,  or  geographical,  miles.  Such  a  comparison  ignores  the 
capacities  of  the  systems  compared,  as  represented  by  addi- 


11 


tional  tracks  and  varying  yard  facilities.  It  is  like  comparing 
two  factories  on  the  basis  of  the  number  of  machines  em¬ 
ployed,  without  reference  to  the  capacity  of  the  same.  Of  late 
years  this  has  been  rectified  in  some  private  and  official  statis¬ 
tics  by  showing,  in  addition  to  route  mileage,  single  track 
mileage,  and,  in  some  cases,  mileage  of  yards  and  sidings. 
Even  when  this  information  is  given,  further  analysis  is  re¬ 
quired  if  jone  is  to  gain  a  useful  idea  as  to  the  real  meaning 
of  the  mileage  to  the  community.  When  comparing  the  mile¬ 
age  of  railways  or  railway  systems,  the  student  needs  always 
to  ask  himself  the  question  as  to  the  extent  to  which  effective 
distribution  of  mileage  has  been  attained,  and  effectiveness  in 
this  case  should  refer  to  tne  general  economic  interests  of  the 
country,  for,  after  all,  sucn  interests  in  the  long  run  underlie 
private  progress  and  success.  The  distribution  of  the  mileage 
is  an  important  consideration,  since,  in  two  regions  of  equal 
area  and  equal  railway  mileage,  the  mileage  may  be  well 
spread  in  one  and  very  badly  spread  in  the  other.  It  is  to 
the  ultimate  economic  interests  of  any  state  or  country  that 
its  railway  mileage  should  be  located  so  as  to  give  reasonable, 
though  not  necessarily  uniformly  equal,  accessibility  to  all 
districts.  Over-concentration  of  mileage  in  one  part,  a  not  un¬ 
common  phenomenon,  is  frequently  accompanied  by  lack  of 
facilities  in  other  parts.  Again,  an  area  intermediate  between 
two  other  areas  may  have  a  fairly  considerable  railway  mile¬ 
age  much  more  calculated  to  serve  the  interests  of  the  other 
areas  than  those  of  its  own.  Mileage  per  unit  of  area  or  per 
unit  of  population  is  a  useful  figure,  hut  incomplete.  Equal¬ 
ity  in  these  respects  may  hide  very  real  differences  of  utility 
and  an  area  with  an  inferior  showing  may  really  be  better 
served. 

TRAFFIC  MEASUREMENT. 

limits  of  space  forbid  much  attention  in  this  article  to  the 
statistics  of  traffic  measurement,  though  the  subject  is  one 
worthy  of  detailed  discussion.  It  is  generally  understood  that, 
for  purposes  of  comparison  of  freight  business,  ton-mileage  is 
a  more  adequate  basis  than  actual  tonnage.  Yet  even  ton-mile¬ 
age  is  unsatisfactory;  its  general  nature  necessarily  deprives 
it  of  efficiency  as  a  measure  where  conditions  are  different,  as 
is  commonly  the  case.  The  tonnage  movement  measured  may 
be  largely  one  of  minerals  “foreign  received”  and  “foreign 
delivered,”  or  it  may  he  largely  one  of  merchandise  locally 
collected  and  distributed.  In  amount  of  work  involved,  in 
value  of  service  to  the  railway,  the  traffic  of  one  road  would 
he  poles  apart  from  that  of  the  other,  but  no  indication  what¬ 
ever  of  these  differences  would  find  expression  in  the  general 
ton-mileage  figures.  In  every  case  of  summarized  statistical 
presentation  of  freight  traffic  conditions  it  should  be  made  an 
invariable  rule  to  show  grouped  commodity  ton-mileage;  in 
most  instances  the  requirements  of  general  comparison  would 
be  met  by  a  classification  into  forest  products,  mine  products, 


12 


agricultural  products,  manufactures,  merchandise  and  miscel¬ 
laneous.  From  statistics  of  this  kind  one  is  able  to  form  a 
fairly  intelligible  idea  of  the  traffic  of  roads  compared  and 
their  relative  importance  in  this  respect,  which  is  more  than 
can  be  said  of  the  lumped  ton-mileage  figures.  A  further  divi¬ 
sion  might  be  made  into  local,  through-originating,  through- 
terminal  and  through-transfer,  understanding  by  these  terms 
the  ton-mileage  of  freight  forwarded  from  and  delivered  to 
stations  on  company’s  system  (local),  forwarded  from  local 
stations  to  “foreign”  points  (through-originating),  received 
at  local  stations  from  “foreign”  points  (through-termnal),  and 
received  from  “foreign”  stations  for  delivery  to  “foreign” 
stations  (through-transfer).  This  would  complicate  some¬ 
what  any  general  tabulation  of  statistics,  but  not  seriously, 
when  the  information  deducible  from  the  addition  is  taken 
into  account.  Briefness  of  exposition  and  economy  of  space 
are  idle  virtues  if  they  are  secured  at  the  expense  of  intelligi¬ 
bility. 

CAPITALIZATION  STATISTICS. 

Capitalization  per  mile  is  a  statistic  which  incompetent 
hands  are  capable  of  badly  *mis-using.  Intrinsically  the  figure 
is  worthless,  for  comparison  useless,  unless  qualified  by  a 
whole  host  of  explanatory  clauses.  Yet  it  is  frequently  used 
in  comparing  costs  of  different  systems.  The  practice  is 
faulty  because  (1)  the  comparison  is  made  on  geographical 
mileage  whereas  the  expenditure  has  been  made  on  track 
mileage,  (2)  the  manipulation  of  capital  in  the  form  of  nomi¬ 
nal  additions  has  varied  considerably  from  system  to  system 
so  that  the  ratios  of  real  costs  are  very  different  from  those 
of  nominal  costs,  (3)  the  existing  extent  of  capital  has  been 
influenced  to  no  small  degree  by  differences  in  policy  as  to 
the  handling  of  betterment  expenditures.  In  any  case,  since 
conditions  of  legal  procedure,  land  acquisition,  labor  supply 
and  so  forth,  vary  most  widely  in  railway  building,  it  is  hard 
to  see  how  much  wiser  one  is  for  knowing  that  Railway  X 
cost  $70,000  a  mile  and  Railway  Y  $250,000,  even  when  ad¬ 
justment  has  been  made  for  artificial  differences  in  capitaliza¬ 
tion.  Certainly,  without  a  very  detailed  knowledge  of  the 
underlying  conditions,  it  would  be  hazardous  to  assert  that 
the  former  road  was  economically  built  and  the  latter  ex¬ 
travagantly.  The  costliness  of  a  machine  is  relative  to  the 
work  it  does,  and  hence,  of  the  two,  the  $70,000  road  may 
happen  to  be  the  extravagantly  built  one. 

Capitalization  statistics  evidence  great  variations  in  capital 
per  mile  of  line,  and  this  fact,  correlated,  as  it  has  been,  with 
spectacular  feats  of  financial  legerdemain  on  the  part  of  cer¬ 
tain  railways,  has  wrought  a  conviction  in  the  minds  of  many 
that  overcapitalization  is  a  common  condition  of  American 
railways,  influencing  unfavorably  the  level  of  rates.  Now  it 
Is  unquestionable  that  considerable  nominal  additions  have 
been  made  to  railway  capital,  but  against  such  increases  need 


13 


be  set  off  the  also  considerable  portions  of  revenue  that  have 
been  expended  in  permanent  improvement,  as  well  as  those 
decreases  in  capital  that  have  occasionally  occurred  in  trans¬ 
fer  of  ownership.  It  is  impossible  to  determine  the  relative 
size  of  these  items,  and  he  is  a  man  of  easy  conviction  who 
is  prepared  to  argue  that,  for  the  railways  of  the  United 
States  as  a  whole,  the  former  is  materially  greater  than  the 
latter.  And  if  it  is,  the  difference  must  be  very  much  less 
than  most  people  credit.  The  previous  statement  infers  that 
the  proper  measure  of  railway  capitalization  is  actual  orig¬ 
inal  investment  in  the  property  plus  the  cost  of  improvements 
whether  paid  for  out  of  capital  or  out  of  revenue.  If  rail¬ 
way  building  were  to  be  started  all  over  again,  the  restric¬ 
tion  of  capitalization  within  these  limits  would  be  justifiable, 
theoretically,  at  any  rate.  It  is  to  the  interest  of  the  in¬ 
vesting  public,  and  of  the  community  at  large,  that  the  real 
profit  capacity  of  every  railway  property  should  be  apparent 
on  the  face  of  its  balance  sheet  and  income  account;  only 
when  capitalization  is  identical  with  actual  investment,  is 
it  practicable  to  keep  track  of  the  real  profitability  of  the 
undertaking.  It  would  surely  seem  that  actual  investment  in 
the  building  and  improvement  of  a  railway  is  the  logical 
basis  of  capitalization,  though  it  may  be  a  very  untenable 
one  from  the  standpoint  of  business  men  and  their  traditional 
methods.  But,  comes  the  objection,  is  it  not  proper,  even 
theoretically,  to  allow  X  or  Y  to  increase  the  capitalization 
of  a  railway  he  purchases  up  to  the  limit  of  the  price  actually 
paid?  Does  not  this  price  represent  to  him  a  real  invest¬ 
ment?  Plausible  though  this  seems,  I  can  hardly  admit  that 
it  is  theoretically  justifiable.  What  X  or  Y  pays  to  secure 
the  profits  to  which  each  certificate  of  the  capitalization  en¬ 
titles  him  represents  his  valuation  of  the  property;  thereby 
he  decides  with  what  rate  of  profit  he  will  be  satisfied.  The 
money  he  pays  goes,  not  into  the  railway,  but  into  the  pocket 
of  its  former  owners.  There  is  no  valid  reason  why  his  valua¬ 
tion  and  what  he  purchases,  namely,  the  investment  of  a 
million  dollars,  or  whatever  it  may  be,  in  the  production  of 
a  certain  utility,  should  be  equalized.  In  fact,  logically  they 
cannot  be.  The  investment  for  the  purpose  of  producing  the 
utility,  and  it  is  immaterial  whether  some  part  of  this  in¬ 
vestment  was  judiciously  made  or  not,  is  one  thing,  and  his 
investment  for  the  purpose  of  securing  the  profits  arising 
out  of  that  utility  is  another.  As  a  matter  of  fact,  the  pur¬ 
poses  underlying  increase  of  capitalization,  following  acquisi¬ 
tion  of  a  property,  are  frequently  those  relating  to  speculative 
trading  or  to  the  concealment  of  rate  of  profit.  This  does 
not  deny  the  justification,  either  at  the  time  of  a  purchase, 
or  at  any  other  time,  of  an  increase  in  capitalization  equal  to 
those  permanent  improvement  expenditures  out  of  the  revenue 
of  the  property  not  previously  taken  into  capital  account,  or, 
of  course,  of  an  increase  in  capitalization  for  the  purpose  of 


14 


securing  funds  which  are  intended  to  be,  and  actually  are, 
sunk  in  the  business.  I  fully  realize  that  the  application  of 
the  theory  flow  stated  would  have  retarded  the  promotion 
and  construction  of  certain  railways,  but  the  history  of  rail¬ 
way  enterprise  in  this  country,  especially  for  the  couple  of 
decades  or  so  following  the  Civil  War,  leads  one  to  believe 
that  this  retardation  might  have  had  advantages  of  its  own, 
and  that  there  would  have  been  less  economic  loss  from  fool¬ 
ish  location  and  unduly  speculative  building. 

A  business  undertaking  is  sometimes  capitalized  at  an 
amount  over  and  above  that  necessary  to  carry  on  the  busi¬ 
ness,- only  a  part  of  the  amount  called  for  by  each  share  being 
actually  subscribed,  this  arrangement  having  advantages  in 
enabling  further  capital  (within  the  limit  of  the  share  lia¬ 
bility)  to  be  obtained  with  certainty,  promptness,  and  fre¬ 
quently  with  economy.  In  such  cases,  the  real  capital  is  the 
subscribed  capital,  and  the  law  should  require  every  official 
statement  of  capitalization  of  such  a  company,  and  every  stock 
exchange  quotation,  to  be  accompanied  by  figures  showing  the 
subscribed  value  of  each  stock  certificate. 

Sufficient  has  been  said  to  indicate  the  rashness  of  a  sweep¬ 
ing  charge  of  overcapitalization,  since  it  is  clear  that  the 
only  real  and  satisfactory  test  of  capitalization  cannot  be 
applied.  This  difficulty  has  induced  financial  writers  to  sug¬ 
gest  the  application  of  cost  of  reproduction  or  of  market 
valuation  of  securities  as  suitable  criteria.  The  latter  is  but 
a  function  of  income-earning  power,  representing  an  averaging 
down  of  profits,  and  bears  no  relation  to  the  investment.  Capi¬ 
talization  on  this  basis  serves  but  to  hide  the  real  profitability 
of  the  investment.  And,  anyhow,  the  market  prices  of  securi¬ 
ties  bought  and  sold  on  the  exchange  form  an  unreliable  guide, 
because  these  are  the  prices  usually  of  but  limited  amounts, 
and  it  by  no  means  follows  that  an  offering  of  the  whole  issue 
at  one  time  would  secure  similar  prices.  Cost  of  reduplica¬ 
tion  is  obtaining  more  favor  than  market  valuation,  but,  ob¬ 
viously,  as  costs  and  conditions  of  construction  are  constantly 
changing,  the  cost  of  reduplication  may  be  far  removed  from 
the  actual  costs,  and  hence  this  fails  as.  an  accurate  criterion. 
Yet  in  the  case  of  the  majority  of  American  railways,  a  phy¬ 
sical  valuation  of  the  existing  property  would  probably  rep¬ 
resent  a  reasonably  fair  maximum  capitalization,  and  capi¬ 
talization  much  in  excess  of  this,  though  not  necessarily  ficti¬ 
tious,  must  be  looked  upon  with  suspicion.  If  phy:icai  valua¬ 
tion  is  to  be  accepted  as  a  satisfactory  test  of  capitalization, 
the  charge  of  general  overcapitalization  must  forthwith  disap¬ 
pear,  as  it  may  safely  be  said  to  be  impossible  to  reproduce 
the  railways  of  the  United  States  for  the  amount  per  mile  rep¬ 
resented  by  their  capitalization. 

The  effect  of  overcapitalization  upon  rates  falls  too  much 
outside  the  scope  of  this  article  to  justify  more  than  a  brief 
reference.  It  is  difficult  to  imagine  that,  under  the  competi- 


15 


tive  conditions  so  characteristic  of  a  large  part  of  the  rail¬ 
way  business  of  the  United  States,  degree  of  capitalization 
can  definitely  influence  transportation  rates.  The  capital  in¬ 
vested  in  railways  is  largely  sunk  once  and  for  all.  Track, 
locomotives,  cars  and  appliances  will  deteriorate,  even  if  not 
used.  Hence,  any  rate  that  returns,  in  the  estimation  of  the 
railway  manager,  somewhat  more  than  sufficient  to  defray 
wear  and  tear  due  to  the  traffic  and  cost  of  transportation 
will  be  better  than  no  traffic.  This  is,  under  ordinary  condi¬ 
tions,  the  nether  limit  of  rates,  a  limit  to  which  they  rarely 
descend,  but  the  existence  of  which,  neverthelezs,  is  powerful 
iu  influencing  the  actual  level  at  which  they  settle.  Such  fav¬ 
orable  conditions  for  the  exercise  of  competition  prevent  the 
railway  manager  from  basing  his  rates  upon  the  capitaliza¬ 
tion.  Thus  it  happens  that,  in  the  case  of  a  group  of  im¬ 
portant  western  roads,  the  one  with  more  than  three  times 
the  capitalization  of  any  of  its  rivals  is  forced,  by  the  exi¬ 
gencies  of  competition,  to  give  even  lower  rates  than  the 
others.  Where  a  condition  of  monopoly  exists,  it  is  possible 
that  overcapitalization  may  have  a  general  effect  upon  rates, 
if  the  rates,  before  the  excess  of  capital  is  superimposed,  are 
such  that  an  appreciable  increase  in  them  would  neither 
lessen  present  traffic  nor  prevent  the  development  of  future 
traffic  to  any  appreciable  extent.  If  the  railway,  under  such 
monopolistic  conditions,  is  already  exacting  the  return  which 
gives  it  the  maximum  net  profit,  then  an  increase  in  rates 
would  be  inconceivable,  as  it  would  slow  down  the  traffic  and 
represent  a  voluntary  reduction  of  profit  to  a  point  below  the 
maximum.  The  conditions  under  which  cases  of  capitaliza¬ 
tion  tend  to  affect  the  general  level  of  rates  are  much  more 
likely  to  occur  in  local  than  in  through  traffic,  but  even  local 
rates  fail  to  show  many  instances  of  increase  that  can  be 
definitely  ascribed  to  manipulation  of  capitalization. 

The  foregoing  survey  of  some  of  the  more  important  rail¬ 
way  statistics  has  been  by  no  means  exhaustive,  but  enough 
has  been  said,  it  is  hoped,  to  emphasize  the  Jimitafion  attach¬ 
ing  to  them,  especially  as  usually  presented,  and  the  necessity 
of  a  careful  and  intelligent  interpretation.  .Neither  railway 
officials  nor  writers  employing  such  statistics  have  always 
exercised  good  judgment  in  this  respect.  Too  frequently  may 
they  be  found  resorting  to  reasoning  which  suggests,  as  a 
well-known  statistician  remarked  some  years  ago,  “a  man 
trying  to  lift  himself  over  a  fence  by  his  boot  straps.”  It 
is,  indeed,  extremely  easy  in  statistical  elaboration  to  pass 
from  one  assumption  to  another  until  out  of  a  mass  of  figures 
certain  results  are  obtained  which  are  accepted  as  precise  and 
accurate  without  recognition  of  their  hypothetical  basis.  Only 
by  extreme  vigilance  can  errors  of  this  kind  be  avoided.  In 
so  far  as  the  previous  discussion  may  act  as  a  reminder  of 
this  “proneness  to  error”  in  statistical  reasoning,  it  will  have 
served  its  purpose. 


16 


